Topics in Dynamical Systems

Lecturer: Omri Sarig, Ziskind, room 261

Time: First Semester, 2024/25, Mondays 16:00-19:00

Place: Ziskind Building, room 1 (in the basement)

Zoom: The lectures are transmitted by zoom, and recorded on Panopto. Registered students are linked automatically.

Unregistered Students who want access to the zoom lectures and their recordings should  email Netta Ram, at Feinberg Graduate School (netta.ram@weizmann.ac.il), and cc me using

Recommended Texts:

  1. Brin and Stuck: Introduction to Dynamical Systems, Cambridge University Press, 2002
  2. Katok and Hasselblatt: Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995

Lecture Notes

  • Lecture 1: Introduction
  • Lecture 2: Review of Point Set Topology (no notes)
  • Lecture 3: Topological Transitivity, Minimality, Kronecker's Theorem
  • Lecture 4: Dynamical Proof of  Van Der Waerden's Theorem 
  • Lecture 5: Review of Measure Theory
  • Lecture 6: Invariant Measures
  • Lecture 7: Ergodicity and Unique Ergodicity
  • Lecture 8: Dynamical Proof of the Uniform Distribution of {n^k alpha}
  • Review of Manifolds
  • Lecture 9: Introduction to Hyperbolic Phenomena
  • Lecture 10: Pesin Charts and Exponential Sensitivity to Initial Conditions
  • Lecture 11: Shadowing Lemma, Closing Lemma, Structural Stability
  • Lecture 12: Invariant Cones and the Stability of Hyperbolic Sets